Three-dimensional integrated circuit

ABSTRACT

A three-dimensional integrated circuit device can include a group of die, a device layer and a thermal interface material formed above the substrate. A heat spreader can be located above the die, the device layer and the thermal interface material. The heat spreader can include a heat pipe comprising a rectangular-shaped heat pipe or disk-shaped heat pipe. A heat sink can be located above the heat spreader. The heat sink can include the heat pipe comprising the rectangular-shaped heat pipe or the disk-shaped heat pipe.

CROSS REFERENCE TO PROVISIONAL APPLICATION

This patent application claims priority under 35 U.S.C. § 119 to U.S.Provisional patent application Ser. No. 63/312,210 which was filed onFeb. 21, 2022, and is incorporated by reference herein in its entirety.

TECHNICAL FIELD

Embodiments are related to integrated circuits. Embodiments are alsorelated to the thermal management of integrated circuits. Embodimentsfurther relate to three-dimensional (3D) integrated circuits.Embodiments additionally relate to heat pipes and in particularflat-shaped heat pipes. Embodiments further relate to methods, systemsand devices that improve the thermal performance of 3D integratedcircuits utilizing rectangular-shaped and/or disk-shaped heat pipes.

BACKGROUND

Moore's law has been applicable for many of the advancements in modernelectronics. The issue of coming up against proper thermal management,however, prevents electrical devices and electrical components frombeing produced in much smaller scales. Hence, the industry has movedfrom a two-dimensional approach to a three-dimensional set-up to utilizethe volume more efficiently. A three-dimensional integrated circuit (3DIC) is a metal-oxide semiconductor integrated circuit manufactured bystacking silicon wafers or dies and interconnecting them verticallyusing through-silicon vias (TSVs), such that they behave as a singleintegrated device to achieve higher performance, lower powerconsumption, higher functional density, lower transistor packagingdensity, and a smaller formfactor than conventional two-dimensionalintegrated circuits.

Despite all these benefits, heat built up within the stacks must beremoved. 3D ICs pack an extraordinary amount of complexity into anextremely small space, which creates a substantial amount of heat,resulting in damage to the device's reliability. Thermal hotspots in 3DICs can exacerbate failure mechanisms such as junction leakage andelectromigration, resulting in degradation of the device's performance.It is increasingly important to have effective and efficient thermalmanagement in order to optimize the design characteristics of 3D ICs.Discussions regarding this topic have dominated research in recentyears. Santos et al., for example, has demonstrated that non-thinnedstacked dies may act as heat spreaders to alleviate hotspot issues. Itwas also proposed in that study that graphite-based heat spreaders canbe used as an alternative to compensate the poor heat dissipationexhibited in 3D ICs [1].

Zhang et al. [2] concluded that the embedded microfluidic cooling showssignificant junction temperature reduction compared to air-cooling byevaluating the hotspot temperature of different architectures of 3D ICsexperimentally. Chiang et al. [3] discussed the thermal performance withvarious integration schemes of 3D ICs and showed that the effects ofvias are crucial in analyzing the thermal performance. Tavakkoli et al.[4, 5] performed a comprehensive thermal analysis of 3D high performancechips using numerical simulations. The effect of parametric changes inthe geometrical configuration on the temperature distribution andhotspot temperature were extensively highlighted, such as size, numberand spacing, TSV arrangements (nominal TSVs, uniform TSVs andcore-concentrated TSVs). The investigation also sufficiently outlinedthe impact of the thermophysical properties of the chip and coolingfluid on the flow and heat transfer. Their results presented the keyfeatures to be used for establishing optimized design and setup of 3DICs. And it was established that a core-concentrated TSV arrangement isthe foremost emplacement of the optimized TSV arrangement in variedcases.

Wang, C., Huang, X. J., & Vafai, K. (2021) [6] performed the heattransfer computational fluid dynamic analysis to study the effects ofgeometric and thermal properties of multilayer nominal 3D IC chips onthe temperature hotspots with different distributions of processors(overlapped cores and staggered cores). They found that the larger thenumber of the chip layers, the higher the hotspot temperature is; buthaving a large Reynolds number can help decrease the hotspottemperature. And with core-concentrated thermal TSVs, the staggeredcores have better thermal performance at a lower number of layers (2-8)while the overlapped core structure performed better at a higher numberof layers (10-18) [6]. Xiao et al. [7] performed the FEA and 3D CFDanalysis under a natural convection environment on the thermalperformance of 3D stacked ICs and proposed a fast and accurate approachto estimate equivalent thermal conductivity of interposer with variousTSV parameters. They advocated that a smaller TSV diameter and SiO₂thickness and a greater TSV pitch will increase the equivalent thermalconductivity in the x-y direction but a smaller TSV pitch and SiO2thickness and a larger TSV diameter will raise the equivalent thermalconductivity in the z direction. It was also mentioned that the maximumjunction temperature difference between each layer of stacked chips isnegligible for the uniform heat source setting, while the thinner chipwould result in noticeable hot spots [7]. However, this conclusion isbased on 3D ICs without heat sinks. With heat sinks, the device layerthat is farthest from heat sink is exposed to a higher temperaturecompared to the device layer that is closer to the heat sinks [4].

Jain et al. [8] developed analytical and finite-element models of heattransfer in stacked 3D ICs to investigate the impact of variousgeometric parameters and thermophysical properties on the thermalperformance. This investigation established that package and heat sinkthermal resistances play a more important role in determining the risein temperature compared to inter-die bond thermal resistances.

Heat sinks are essentially heat dissipation devices for removing heatfrom a heat source, such as processors and GPUs, to keep the source at aproper operating temperature. Heat sinks are crucial in optimizing thethermal performance of 3D ICs. Heat pipes can be excellent heat sinksand have been contributing to the thermal management in existingintegrated circuit technology. A heat pipe is a vacuum sealed metal tubethat contains a working fluid that changes from liquid to vapor whenheat is applied to one end of the tube. The heated vapor moves quicklyto the other end of the tube where it condenses then travels through thewick material (sintered copper) back to the heat source section. Thisdesign allows heat pipes to transfer heat much more efficiently than asolid piece of metal with the added benefits of being much lighterweight and performing well in any orientation.

It has been well established in many applications, such as spacecraftthermal controls, electronic systems cooling and many commercial thermaldevices. However, the traditional heat pipes have some limitations; forinstance, they only transfer heat in one direction and the round shapemakes it physically difficult to get close to a very small heat source.Vafai et al. [9-13] had established and analyzed comprehensivelyflat-shaped heat pipes that can overcome the limitations of thetraditional heat pipes. The flat-shaped heat pipes offer an effectivesolution for the high heat generation of 3D ICs and have far-reachingimpact on the thermal management of 3D ICs with unrivaled advantages,such as a secondary feeding mechanism, substantially better geometricadoptability for complex applications and ability to fully handle theasymmetrical heat load.

BRIEF SUMMARY

The following summary is provided to facilitate an understanding of someof the innovative features unique to the disclosed embodiments and isnot intended to be a full description. A full appreciation of thevarious aspects of the embodiments disclosed herein can be gained bytaking the entire specification, claims, drawings, and abstract as awhole.

It is, therefore, one aspect of the disclosed embodiments to provide foran improved integrated circuit.

It is another aspect of the disclosed embodiments to provide the thermalmanagement of integrated circuits.

It is a further aspect of the embodiments to provide for an improved 3Dintegrated circuit.

It is also an aspect of the embodiments to provide for utilization of aflat-shaped heat pipe as a thermal management strategy for a 3Dintegrated circuit and other devices.

It is a further aspect of the embodiments to provide for an innovativerectangular-shaped or disk-shaped heat pipe as a heat sink for 3Dintegrated circuits.

It is also an aspect of the embodiments to provide for an innovativemethod, apparatus and system that uses a flat-shaped heat pipe as a heatspreader and a heat sink in a single 3D IC structure.

The aforementioned aspects and other objectives and advantages can nowbe achieved as described herein. In an embodiment, a 3D integratedcircuit device, can include: a substrate; a plurality of die, a devicelayer and a thermal interface material formed above the substrate; aheat spreader located above the plurality of die, the device layer andthe thermal interface material, the heat spreader comprising a heat pipecomprising a rectangular-shaped heat pipe or disk-shaped heat pipe; anda heat sink located above the heat spreader, the heat sink comprisingthe heat pipe comprising the rectangular-shaped heat pipe or thedisk-shaped heat pipe.

In an embodiment, a 3D integrated circuit device can include asubstrate; a thermal interface material layer; a plurality of die, adevice layer and a micro-bump thermal interface material layer formedabove thermal interface material layer; a heat spreader located abovethe plurality of die, the device layer and the thermal interfacematerial, the heat spreader comprising a heat pipe comprising arectangular-shaped heat pipe or disk-shaped heat pipe; and a heat sinklocated above the heat spreader, the heat sink comprising the heat pipecomprising the rectangular-shaped heat pipe or the disk-shaped heatpipe. In an embodiment, the thermal interface layer can comprise a C4bump (or C4 bumps).

In an embodiment, a 3D integrated circuit device, can include asubstrate; a thermal interface material layer comprising C4 bumps; aplurality of die, a device layer and a micro-bump thermal interfacematerial layer formed above the C4-bump thermal interface materiallayer; a heat spreader located above the plurality of die, the devicelayer and the thermal interface material, the heat spreader comprising aheat pipe comprising a rectangular-shaped heat pipe or disk-shaped heatpipe; and a heat sink located above the heat spreader, the heat sinkcomprising the heat pipe comprising the rectangular-shaped heat pipe orthe disk-shaped heat pipe.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying figures, in which like reference numerals refer toidentical or functionally-similar elements throughout the separate viewsand which are incorporated in and form a part of the specification,further illustrate the present invention and, together with the detaileddescription of the invention, serve to explain the principles of thepresent invention.

FIG. 1 illustrates a schematic diagram of the structure of athree-dimensional IC, in accordance with an embodiment;

FIG. 2 illustrates a cross-sectional view of a rectangular-shaped ordisk-shaped heat pipe, in accordance with an embodiment;

FIG. 3 illustrates a graph depicting data resulting from a gridindependence study for the investigated geometries, in accordance withan embodiment;

FIG. 4 illustrates a graph depicting data indicative of a comparison ofthe temperature distribution for the nominal benchmark 3D IC withTavakkoli et al. [4,5] (a) along the x direction for each device layer(b) along the y direction for each device layer (c) along the zdirection at the vertical center line of each core and the center lineof chip, in accordance with an embodiment;

FIG. 5 illustrates a graph depicting data indicative of a comparison ofthe effects of different TSV arrangement on the temperature distributionof the 3D IC structure with Tavakkoli et al. [4, 5] (a) along the xdirection in device layer 1 (b) along the y direction in device layer 1(c) along the z direction at vertical center line of the core processor3, in accordance with an embodiment;

FIG. 6 illustrates a graph depicting data indicative of a comparison ofthe hotspot temperature with the experimental results, in accordancewith an embodiment;

FIG. 7 illustrates a graph depicting data indicative of a comparison ofthe vapor and liquid pressure distributions along the heat pipe;

FIG. 8 illustrates a graph depicting data indicative of a comparison ofthe vapor temperature profiles for different injection Reynolds numbers,in accordance with an embodiment;

FIG. 9 illustrates a graph depicting data indicative of a Device layer 1temperature distribution for different lengths of the heat sinks (a)Copper heat sink (b) rectangular-shaped heat pipe (c) disk-shaped heatpipe, in accordance with an embodiment;

FIG. 10 illustrates a graph depicting data indicative of the effect ofthe lengths of the heat sink and flat-shaped heat pipes on the hotspottemperature for a nominal 3D IC structure, in accordance with anembodiment;

FIG. 11 illustrates a graph depicting data indicative of the effect ofthe flat-shaped heat pipe on the hotspot temperature of a typical 3D ICfor heat dissipation powers, in accordance with an embodiment;

FIG. 12 illustrates a graph depicting data indicative of the effect ofdifferent configurations of the rectangular-shaped heat pipe on thehotspot temperature of a typical 3D IC configuration, in accordance withan embodiment;

FIG. 13 illustrates a graph depicting data indicative of thermalresistance of different heat sinks implemented in the 3D IC, inaccordance with an embodiment; and

FIG. 14 illustrates a graph depicting data indicative of the effect of aflat-shaped heat pipe as the heat spreader on the hotspot temperature ofa 3D IC, in accordance with an embodiment.

DETAILED DESCRIPTION

The particular values and configurations discussed in these non-limitingexamples can be varied and are cited merely to illustrate one or moreembodiments and are not intended to limit the scope thereof.

Subject matter will now be described more fully hereinafter withreference to the accompanying drawings, which form a part hereof, andwhich show, by way of illustration, specific example embodiments.Subject matter may, however, be embodied in a variety of different formsand, therefore, covered or claimed subject matter is intended to beconstrued as not being limited to any example embodiments set forthherein; example embodiments are provided merely to be illustrative.Likewise, a reasonably broad scope for claimed or covered subject matteris intended. Among other things, for example, subject matter may beembodied as methods, devices, components, or systems. Accordingly,embodiments may, for example, take the form of hardware, software,firmware, or any combination thereof (other than software per se). Thefollowing detailed description is, therefore, not intended to beinterpreted in a limiting sense.

Throughout the specification and claims, terms may have nuanced meaningssuggested or implied in context beyond an explicitly stated meaning.Likewise, phrases such as “in one embodiment” or “in an exampleembodiment” and variations thereof as utilized herein do not necessarilyrefer to the same embodiment and the phrase “in another embodiment” or“in another example embodiment” and variations thereof as utilizedherein may or may not necessarily refer to a different embodiment. It isintended, for example, that claimed subject matter include combinationsof example embodiments in whole or in part. In addition, identicalreference numerals utilized herein with respect to the drawings canrefer to identical or similar parts or components.

In general, terminology may be understood, at least in part, from usagein context. For example, terms such as “and,” “or,” or “and/or” as usedherein may include a variety of meanings that may depend, at least inpart, upon the context in which such terms are used. Typically, “or” ifused to associate a list, such as A, B, or C, is intended to mean A, B,and C, here used in the inclusive sense, as well as A, B, or C, hereused in the exclusive sense. In addition, the term “one or more” as usedherein, depending at least in part upon context, may be used to describeany feature, structure, or characteristic in a singular sense or may beused to describe combinations of features, structures, orcharacteristics in a plural sense. Similarly, terms such as “a,” “an,”or “the”, again, may be understood to convey a singular usage or toconvey a plural usage, depending at least in part upon context. Inaddition, the term “based on” may be understood as not necessarilyintended to convey an exclusive set of factors and may, instead, allowfor existence of additional factors not necessarily expressly described,again, depending at least in part on context.

Rectangular-shaped and disk-shaped heat pipes, as innovative heat sinks,can be used to optimize the thermal performance of three-dimensionalintegrated circuits (3D ICs). Finite volume numerical analysis can beemployed to carry out the simulation of the thermal performance of 3DICs. Both rectangular-shaped and disk-shaped heat pipes cansubstantially improve the overall thermal performance and reduce thehotspot temperatures by, for example, 7 K and 11 K on average,respectively. Furthermore, utilizing the rectangular-shaped or thedisk-shaped heat pipe embodiments as a heat spreader in place of a solidcopper heat spreader can further optimize the thermal performance byreduction of the junction temperatures, for example, 14 K and 16 K onaverage, respectively. These reductions can be achieved while the weightof the set-up can be also significantly reduced. The results indicatethat the disclosed innovative flat-shaped heat pipes can significantlyoptimize the thermal performance of 3D ICs. The model and resultsdiscussed herein aim to pave the way to markedly alleviate the thermalissues of 3D ICs.

The embodiments relate to the utilization of flat-shaped heat pipes asheat sinks and heat spreaders on the thermal performance of 3D ICs witha core-concentrated TSVs arrangement. A significant effect offlat-shaped heat pipes on the reduction of junction temperature and theoverall thermal performance of the 3D IC structure may be improvedthrough implementation of the embodiments.

FIG. 1 illustrates a schematic diagram of the structure of athree-dimensional IC, in accordance with an embodiment. The schematic ofthe nominal 3D IC structure is shown in FIG. 1 as shown in Tavakkoli etal. [4, 5]. As can be seen, the 3D IC structure incorporates asubstrate, a thermal interface material (TIM) layer with C4 bumps, threelayers of dies, device layers and thermal interface materials withmicrobumps, a heat spreader and a flat-shaped heat pipe as the heatsink. Device layers, bonded between TIM with microbumps and die,comprises four processors which are the main heat. Table 1 displays thenominal values for different components of the 3D IC structure,including materials, length and width, and thickness.

The nominal heat dissipation (30 W each layer) produced by thetransistors in the processors, are conducted through the layers to thesubstrate downward and to the heat spreader, and subsequently dissipatedto the heat sink upward and eventually to the ambient air throughconvective heat transfer. Conductive heat transfer through the solid,and isotropic layers of the 3D IC are governed by:

$\begin{matrix}{{\frac{\partial^{2}\Theta_{s}^{+}}{\partial x^{+ 2}} + \frac{\partial^{2}\Theta_{s}^{+}}{\partial y^{+ 2}} + \frac{\partial^{2}\Theta_{s}^{+}}{\partial z^{+ 2}} + q_{g}^{+}} = 0} & (1)\end{matrix}$

Where q_(g) ⁺ denotes the dimensionless volumetric heat generation inthe central processing units and the nondimensionalized temperature andcoordinates are set up as:

${x^{+} = \frac{x}{h}},$ ${y^{+} = \frac{y}{h}},$${z^{+} = \frac{z}{h}},$ $\Theta^{+} = \frac{T - T_{e}}{{qh}/k_{f}}$

The natural convective heat transfer is replayed at the bottom surfaceof the substrate, whereas the forced convection is administered at thetop surface of the flat-shaped heat pipes. The convective boundaryconditions are:

$\begin{matrix}{\frac{\partial\Theta_{s}^{+}}{\partial n} = {{- {Bi}} \cdot \Theta_{s}^{+}}} & (2)\end{matrix}$

Where n is the normal coordinate and Bi is the dimensionless Biotnumber.

The heat transfer and fluid flow are based on the Navier-stokesequations. The cooling fluid enters into the 3D IC package at ambienttemperature with a specified Reynolds number and exits the package atatmospheric pressure with negligible streamwise temperature change. Thedimensionless Navier-Stokes equations in Cartesian coordinates are:

Mass Conservation:

$\begin{matrix}{{\frac{\partial u^{+}}{\partial x^{+}} + \frac{\partial v^{+}}{\partial y^{+}} + \frac{\partial w^{+}}{\partial z^{+}}} = 0} & (3)\end{matrix}$

x-Momentum Equation:

$\begin{matrix}{{{Re}_{h}\left( {{u^{+}\frac{\partial u^{+}}{\partial x^{+}}} + {v^{+}\frac{\partial u^{+}}{\partial y^{+}}} + {w^{+}\frac{\partial u^{+}}{\partial z^{+}}}} \right)} = {{- \frac{\partial p^{+}}{\partial x^{+}}} + \left( {\frac{\partial^{2}u^{+}}{\partial x^{+ 2}} + \frac{\partial^{2}u^{+}}{\partial y^{+ 2}} + \frac{\partial^{2}u^{+}}{\partial z^{+ 2}}} \right)}} & (4)\end{matrix}$

y-Momentum Equation:

$\begin{matrix}{{{Re}_{h}\left( {{u^{+}\frac{\partial v^{+}}{\partial x^{+}}} + {v^{+}\frac{\partial v^{+}}{\partial y^{+}}} + {w^{+}\frac{\partial v^{+}}{\partial z^{+}}}} \right)} = {{- \frac{\partial p^{+}}{\partial y^{+}}} + \left( {\frac{\partial^{2}v^{+}}{\partial x^{+ 2}} + \frac{\partial^{2}v^{+}}{\partial y^{+ 2}} + \frac{\partial^{2}v^{+}}{\partial z^{+ 2}}} \right)}} & (5)\end{matrix}$

z-Momentum Equation:

$\begin{matrix}{{{Re}_{h}\left( {{u^{+}\frac{\partial w^{+}}{\partial x^{+}}} + {v^{+}\frac{\partial w^{+}}{\partial y^{+}}} + {w^{+}\frac{\partial w^{+}}{\partial z^{+}}}} \right)} = {{- \frac{\partial p^{+}}{\partial z^{+}}} + \left( {\frac{\partial^{2}w^{+}}{\partial x^{+ 2}} + \frac{\partial^{2}w^{+}}{\partial y^{+ 2}} + \frac{\partial^{2}w^{+}}{\partial z^{+ 2}}} \right)}} & (6)\end{matrix}$

Energy Conservation for the Fluid Domain:

$\begin{matrix}{{{Pe}_{h}\left( {{u^{+}\frac{\partial\Theta_{f}^{+}}{\partial x^{+}}} + {v^{+}\frac{\partial\Theta_{f}^{+}}{\partial y^{+}}} + {w^{+}\frac{\partial\Theta_{f}^{+}}{\partial z^{+}}}} \right)} = {\frac{\partial^{2}\Theta_{f}^{+}}{\partial x^{+ 2}} + \frac{\partial^{2}\Theta_{f}^{+}}{\partial y^{+ 2}} + \frac{\partial^{2}\Theta_{f}^{+}}{\partial z^{+ 2}}}} & (7)\end{matrix}$

The Nondimensionalized Terms in the Above Equations are:

${u^{+} = \frac{u}{u_{m}}},{v^{+} = \frac{v}{v_{m}}},{w^{+} = \frac{w}{w_{m}}},{p^{+} = \frac{ph}{\mu_{f}u_{m}}},{{Re}_{h} = \frac{\rho_{f}u_{m}h}{\mu_{f}}},{{Pe}_{h} = \frac{\rho_{f}c_{p,f}u_{m}h}{k_{f}}}$

FIG. 2 illustrates a cross-sectional view of a heat pipe, in accordancewith an embodiment. The design and set up of a rectangular-shaped ordisk-shaped heat pipe in previous works of Vafai et al. [9-13] aredeployed in this work. The cross section view of the heat pipe isdisplayed as FIG. 2 . The assumptions made in this model are: (1) Vaporand liquid flow are steady, laminar and subsonic. (2) Transportproperties for the vapor and liquid are taken as constant. (3) The vaporinjection and suction rate are uniform in the evaporator and condensersections. (4) The vapor velocity component in the z direction isnegligible since there is no injection or suction on vertical wicks.

The analytical solution for the vapor pressure distribution, liquidpressure distribution and temperature distribution for therectangular-shaped heat pipe and disk-shaped heat pipe are documented inVafai et al. [9-13]. Based on the analysis given in these works, we canobtain the rectangular and disk-shaped vapor and liquid pressure andtemperature distributions, as given in eqs. (8) to (14) which are usedto validate our model.

Rectangular-Shaped Heat Pipe's Vapor Pressure Distribution

$\begin{matrix}{{\Delta{p_{v}^{+}\left( x^{+} \right)}} = \left\{ \begin{matrix}\begin{matrix}{{- \frac{4\left( {1 - \varphi} \right)}{\left( {2 - \varphi} \right)}}{Re}_{h}\left\{ {{\left\lbrack {{\frac{16\left( {1 - \varphi} \right)}{25\varphi}{Re}_{h}} + \frac{1}{2\left( h_{b}^{+} \right)^{2}}} \right\rbrack\left( x^{+} \right)^{2}} +} \right.} \\\left. {{\int}_{0}^{x^{+}}\frac{x^{+}}{{f^{+}\left( x^{+} \right)}\left( {1 - {f^{+}\left( x^{+} \right)}} \right)}{dx}^{+}} \right\} \\\left( {0 \leq x^{+} \leq {\varphi l^{+}}} \right)\end{matrix} \\\begin{matrix}{{\Delta{p\left( {\varphi l^{+}} \right)}} - {\frac{4\varphi}{\left( {2 - \varphi} \right)}{Re}_{h}\left\{ \left\lbrack {{\frac{16\varphi}{25\left( {2 - \varphi} \right)}{Re}_{h}} - \frac{1}{2\left( h_{b}^{+} \right)^{2}}} \right\rbrack \right.}} \\{\left\lbrack {\left( {x^{+} - l^{+}} \right)^{2} - \left( {{\varphi l^{+}} - l^{+}} \right)^{2}} \right\rbrack -} \\\left. {{\int}_{0}^{x^{+}}\frac{x^{+} - l^{+}}{{f^{+}\left( x^{+} \right)}\left( {1 - {f^{+}\left( x^{+} \right)}} \right)}{dx}^{+}} \right\} \\\left( {{\varphi l^{+}} \leq x^{+} \leq l^{+}} \right)\end{matrix}\end{matrix} \right.} & (8)\end{matrix}$

Where f⁺(x⁺) can be found from:

$\begin{matrix}{\frac{{df}^{+}\left( x^{+} \right)}{{dx}^{+}} = \left\{ \begin{matrix}\begin{matrix}\left\lbrack {{{- \frac{9}{2}}\left( {1 - \varphi} \right){f^{+}\left( x^{+} \right)}} +} \right. \\{\left. {{5\frac{\left( {2 - \varphi} \right)}{{Re}_{h}}\frac{1}{f^{+}\left( x^{+} \right)}} - {\frac{5}{2}\varphi}} \right\rbrack\frac{1}{\left( {1 - \varphi} \right)x^{+}}}\end{matrix} & \left( {0 \leq x^{+} \leq {\varphi l^{+}}} \right) \\\begin{matrix}\left\lbrack {{{- \varphi}{f^{+}\left( x^{+} \right)}} +} \right. \\{\left. {10\frac{\left( {2 - \varphi} \right)}{{Re}_{h}}\frac{1}{f^{+}\left( x^{+} \right)}} \right\rbrack\frac{1}{7{\varphi\left( {l^{+} - x^{+}} \right)}}}\end{matrix} & \left( {{\varphi l^{+}} \leq x^{+} \leq l^{+}} \right)\end{matrix} \right.} & (9)\end{matrix}$

Rectangular-Shaped Heat Pipe's Liquid Pressure Distribution

$\begin{matrix}{{\Delta{p_{l}^{+}\left( x^{+} \right)}} = \left\{ \begin{matrix}\begin{matrix}{{\Delta p_{v}^{+}\left( l^{+} \right)} - {\frac{h_{w}^{+}{\mu^{+}\left( {1 - \varphi} \right)}{Re}_{h}}{2\left( {2 - \varphi} \right)K^{+}}\left\{ {{\varphi\left( {1 - \varphi} \right)\left( l^{+} \right)^{2}} +} \right.}} \\\left. \left\lbrack {\left( {\varphi l^{+}} \right)^{2} - \left( x^{+} \right)^{2}} \right\rbrack \right\}\end{matrix} \\\left( {0 \leq x^{+} \leq {\varphi l^{+}}} \right) \\\begin{matrix}{{\Delta{p_{v}^{+}\left( l^{+} \right)}} - {\frac{h_{w}^{+}\mu^{+}\varphi{Re}_{h}}{2\left( {2 - \varphi} \right)K^{+}}\left( {l^{+} - x^{+}} \right)^{2}}} & \left( {{\varphi l^{+}} \leq x^{+} \leq l^{+}} \right)\end{matrix}\end{matrix} \right.} & (10)\end{matrix}$

Rectangular-Shaped Heat Pipe's Temperature Distribution

$\begin{matrix}{{\Delta{T_{v}^{+}\left( x^{+} \right)}} = {\left( T_{ov}^{+} \right)^{2}\left\lbrack \frac{{\ln{p_{v}^{+ 2}\left( x^{+} \right)}} - {\ln p_{ov}^{+}}}{1 - {T_{ov}^{+}\left( {{\ln p_{ov}^{+}} - {\ln{p_{v}^{+}\left( x^{+} \right)}}} \right)}} \right\rbrack}} & (11)\end{matrix}$

Disk-Shaped Heat Pipe's Vapor Pressure Distribution

$\begin{matrix}{{p_{v}^{+}\left( r^{+} \right)} = \left\{ \begin{matrix}\begin{matrix}{{p_{v}^{+}(0)} - {\frac{24}{25}\left( {\frac{1 - \varphi^{2}}{2 - \varphi^{2}}{Re}_{h}R^{+}} \right)^{2}\left( \frac{r^{+}}{R^{+}} \right)^{2}}} & \left( {0 \leq r^{+} \leq {\varphi R^{+}}} \right)\end{matrix} \\\begin{matrix}{{p_{v}^{+}(0)} - {\frac{8}{25}{\left( {\frac{\varphi^{2}}{2 - \varphi^{2}}{Re}_{h}R^{+}} \right)^{2}\left\lbrack {{3\left( \frac{r^{+}}{R^{+}} \right)^{2}} + \left( \frac{R^{+}}{r^{+}} \right)^{2}} \right.}}} \\\left. {{{- 4}\ln\frac{r^{+}}{R^{+}}} - {2\left( {3 - {2\ln\varphi} - \frac{1}{\varphi^{2}}} \right)}} \right\rbrack \\\left( {{\varphi R^{+}} \leq r^{+} \leq R^{+}} \right)\end{matrix}\end{matrix} \right.} & (12)\end{matrix}$

Disk-Shaped Heat Pipe's Liquid Pressure Distribution

$\begin{matrix}{{p_{l}^{+}\left( r^{+} \right)} = \left\{ \begin{matrix}\begin{matrix}{{p_{v}^{+}(0)} + {\frac{v^{+}{{Re}_{h}\left( R^{+} \right)}^{2}}{4{K^{+}\left( h_{w}^{+} \right)}^{3}}{\frac{1 - \varphi^{2}}{2 - \varphi^{2}}\left\lbrack {\left( \frac{r^{+}}{R^{+}} \right)^{2} + {\frac{2\varphi^{2}}{2 - \varphi^{2}}\ln\varphi}} \right\rbrack}} -} \\{\left( {\frac{4}{5}\frac{\varphi^{2}{Re}_{h}}{2 - \varphi^{2}}R^{+}} \right)^{2}\left( {{2\ln\varphi} + \frac{1}{\left. {\varphi^{2} - 1} \right)}} \right.} \\\left( {0 \leq r^{+} \leq {\varphi R^{+}}} \right)\end{matrix} \\\begin{matrix}{{p_{v}^{+}(0)} + {\frac{v^{+}{{Re}_{h}\left( R^{+} \right)}^{2}}{4{K^{+}\left( h_{w}^{+} \right)}^{3}}{\frac{\varphi^{2}}{2 - \varphi^{2}}\left\lbrack {1 - \left( \frac{r^{+}}{R^{+}} \right)^{2} - {2{\ln\left( \frac{R^{+}}{r^{+}} \right)}}} \right\rbrack}} -} \\{\left( {\frac{4}{5}\frac{\varphi^{2}{Re}_{h}}{2 - \varphi^{2}}R^{+}} \right)^{2}\left( {{2\ln\varphi} + \frac{1}{\varphi^{2}} - 1} \right)} \\\left( {{\varphi R^{+}} \leq r^{+} \leq R^{+}} \right)\end{matrix}\end{matrix} \right.} & (13)\end{matrix}$

Disk-Shaped Heat Pipe's Temperature Distribution

$\begin{matrix}{{\Delta{T_{v}^{+}\left( r^{+} \right)}} = {\left( T_{ov}^{+} \right)^{2}\left\lbrack \frac{{\ln{p_{v}^{+}\left( r^{+} \right)}} - {\ln p_{ov}^{+}}}{1 - {T_{ov}^{+}\left( {{\ln p_{ov}^{+}} - {\ln{p_{v}^{+}\left( r^{+} \right)}}} \right)}} \right\rbrack}} & (14)\end{matrix}$

Once the vapor pressure distribution is found, the vapor temperaturedistribution within the heat pipe can be obtained from equations (11)and (14). The temperature difference across the heat pipe may beemployed to calculate the effective thermal conductivity of therectangular-shaped heat pipe and disk-shaped heat pipe with the Eqs.(15) and (16) [14].

$\begin{matrix}{k_{eff} = \frac{{QL}_{eff}}{A\Delta T}} & (15)\end{matrix}$ $\begin{matrix}{L_{eff} = {\frac{L_{evaporator} + L_{condenser}}{2} + L_{adiabatic}}} & (16)\end{matrix}$

Where k_(eff) is the effective thermal conductivity; Q is the powertransported; L_(eff) is the effective length; A is the cross-sectionalarea; ΔT is the temperature difference between evaporator and condensersections. In this study, the evaporator section is on the bottom surfaceof the heat pipe and the rest of the heat pipe's external area acts asthe condenser section [9]. Once the effective thermal conductivity isobtained, the heat pipe employed for the 3D IC structure will be modeledas a solid flat plate in the system. It should be noted that therectangular shaped and disk-shaped heat pipes not only possess theextraordinary heat transfer capacity and rate, but also lighter inweight when compared to solid copper of the same size. This makes theiruse even more appealing. The nominal dimension of the heat pipe is50×50×29.4 mm³ in this investigation, in which the total height of thewick structure is 4 mm. The rest of the volume is a vapor channel, whichis negligible in weight. Compared to the same sized solid copper plate,the weight of the heat pipe is over 7 times lighter.

COMSOL Multiphysics can be utilized to set up the simulations. For modelvalidation, a grid independence study was executed for all investigatedgeometries and the junction temperature for each geometry was evaluatedusing computational meshes for different cell distributions. FIG. 3presents the grid independence study for the nominal cases applyingcustomized coarser, coarse, normal and fine mesh distributions. It canbe concluded that there is no advantage to further increasing the numberof grid cells after coarse mesh distribution. The last refined meshgives a relative difference of %0.02 for the hotspot temperature incomparison with the prior mesh. To minimize the computational cost whilemaintaining the accuracy of the simulation, the coarse mesh distributionis applied in this study.

To ratify the model, the temperature distribution of the 3D IC isvalidated with both the previous simulation work [4] and theexperimental results [2]. The vapor pressure distribution, liquidpressure distribution and temperature distribution within therectangular-shaped heat pipe is compared with the comprehensiveanalytical solution of Vafai and Wang [9].

FIG. 4 illustrates the resemblance of the temperature distribution forthe nominal benchmark 3D IC along the x, y, and z directions for eachdevice layer between the work of Tavakkoli et al. [4] and the presentwork. FIG. 5 displays the comparison of the effect of different TSVarrangements on the temperature distribution of the 3D IC structurealong the x, y and z directions in the device layer 1. It should berecognized that the z direction is at the vertical center line of thecore processor 3. The comparisons between these two works show very goodagreement.

The model is further validated by the experimental results obtained byZhang et al. [2], where the setup model is similar with our simulationmodel. Zhang et al. [2] set up the air-cooled 3D IC stack with twolayers of stacked processors instead of three for the current simulationmodel. For the validation purpose, the simulation of two layers ofstacked processors are implemented to compare the hotspot temperature inthe simulation model with the experimental results. FIG. 6 substantiatesthe validation of the 3D IC model setup used in the research work. FIG.7 and FIG. 8 exhibit a comparison of our results for the flat-shapedheat pipes with the comprehensive analytical results acquired by Vafai &Wang [9].

The temperature distribution of a 3D IC deploying a copper heat sink, arectangular-shaped heat pipe and a disk-shaped heat pipe with differentheat sink lengths for device layer 1 is investigated. It was concludedin the work of Tavakkoli et al. [4] that the junction temperature ismanifested in device layer 1. It should be emphasized that thecore-concentrated TSV arrangement is employed throughout the study. Thesame study from Tavakkoli et al. [4] unveiled that the core-concentratedTSV is superior to the other employments of the optimized TSVarrangement. The current investigation is aimed to optimize the thermalperformance based on the foremost employment with the preeminentperformance in the previous work. As seen from FIG. 9 , as the length ofthe heat sinks increases, the temperature decreases for all three heatsinks. It is evident that the temperature of the 3D IC dropssignificantly when the heat sink length increases from 50 mm to 100 mm.The rate of temperature deduction is slower as the length increasesfurther. FIGS. 9(b) and (c) highlights the substantial effect of therectangular-shaped and disk-shaped heat pipe on the performance of a 3DIC. The rectangular-shaped heat pipe improved the thermal performance byreducing the temperature by 8 degrees in all lengths compared to thecopper heat sink. As it was strengthened in Vafai et al. investigations[9-13], the disk-shaped heat pipe showed more advanced performance thanthe rectangular-shaped heat pipe. With the fixed contact surface area,FIG. 9(c) demonstrated a 16 degrees reduction in temperature when thelength of the heat sink is 50 mm (R=28 mm for the disk-shaped heat pipe)and an average 10 degrees in other lengths compared to the copper heatsink. These findings reveal that both the rectangular-shaped anddisk-shaped heat pipe contribute to the optimization of the thermalperformance of the 3D IC by maximizing the heat conduction andminimizing the temperature rise in the 3D ICs.

FIG. 10 further unveils a comparison of different lengths of aflat-shaped heat pipe and a copper heat sink on the hotspot temperatureof the 3D IC. The hotspot temperature declines remarkably when therectangular-shaped heat pipe and disk-shaped heat pipe are implementedin the 3D IC structure. As anticipated, the disk-shaped heat pipeperforms superior to rectangular-shaped one at all lengths. There isconsiderable drop in the hot spot temperature when using a flat shapedheat pipe as compared with a copper heat sink. In addition, as mentionedearlier we also have the advantage of a substantial reduction in theweight when using the flat-shaped heat pipes for the 3D IC set up.

FIG. 11 demonstrates the effect of increasing the heat dissipation onthe hotspot temperature of a typical 3D IC utilizing a flat-shaped heatpipe compared with a copper heat sink. The allowed operating temperaturefor 11^(th) Gen Intel Core™ i7 & i9 is 373 K. The 3D IC with a copperheat sink is heated up to 393.45 K at a power of 300 W resulting in thetermination of the 3D IC, while the 3D IC with a rectangular flat-shapedheat pipe can operate under 300 W heat dissipation and the one executedwith a disk-shaped heat pipe can reach nearly 400 W. These dataestablish the powerful effect of both the rectangular-shaped anddisk-shaped heat pipes on the junction temperature for high-powerprocessors.

For a typical fixed contact surface area 10,000 mm², the hotspottemperature for different configurations of a rectangular-shaped heatpipe is investigated (50×200 mm², 60×167 mm², 70×143 mm², 80×125 mm²,90×112 mm², 100×100 mm²). FIG. 12 illustrates a moderate temperaturedrop of 2 K when using a square shaped flat-shaped heat pipe. That isthe square shaped heat pipe (100×100 mm²) carries the premier thermalperformance for 3D IC.

The thermal resistances of the three different heat sinks are probed. Asit can be observed from FIG. 13 , the average thermal resistance for thecopper heat sink is about 0.104 K/W, while it is 0.0004 K/W forrectangular shaped heat pipe and almost zero for the disk-shaped heatpipe, respectively. These details authenticated the outstandingperformance of the flat-shaped heat pipes compared to a copper heatsink.

FIG. 14 presents the effects of the flat-shaped heat pipe as a heatspreader on the hotspot temperature. The size of the flat-shaped heatpipe as the heat spreader employed in the simulation is 50×50×3 mm³(R=28 mm for disk-shaped one) with the effective thermal conductivity of5000 W/m·K. The copper heat sink, rectangular-shaped heat pipe heat sinkand disk-shaped heat pipe heat sink are administered on top of thecopper heat spreader, rectangular-shaped heat pipe heat spreader anddisk-shaped heat pipe heat spreader, respectively. It is seen that usinga much lighter weight flat-shaped heat pipe as the heat spreader has avery substantial effect on the hotspot temperature of 3D ICs as opposedto a copper heat spreader of the same size. For a 3D IC with the heatsink length and width 100×100 mm², the hotspot temperature using thecopper heat sink with the copper heat spreader reaches 321.48 K, whilethe one applying rectangular heat pipes as the heat sink and the heatspreader reduces the hotspot temperature by over 13 K and the oneutilizing the disk-shaped heat pipes as the heat sink and the heatspreader further enhances the thermal performance by decreasing thehotspot temperature by almost 17 K.

The optimization and the thermal performance and management of 3D ICsutilizing the innovative rectangular-shaped and disk-shaped heat pipesis investigated in this work. The effects of these innovative flatshaped heat pipes on the temperature distribution and hotspots isexplored in detail. All the models investigated in this work wererigorously validated with established analytical and experimentalresults. The thermal performance and management of therectangular-shaped and disk-shaped heat pipe as heat sinks and heatspreaders for usage in 3D IC structures were analyzed in detail andtheir effectiveness were compared with the current use of copper heatsinks and copper heat spreaders. We have established that theflat-shaped heat pipes substantially reduce the temperature distributionand the hotspot temperature. The following conclusions were corroboratedin the present work:

Both the rectangular-shaped and disk-shaped heat pipes substantiallylower the hotspot temperatures. The rectangular-shaped heat pipe broughtdown the hotspot temperature by 8° C., the disk-shaped heat pipe canlower it by about 16° C. They offer this sizeable advantage while the 3DIC structure's weight at the same time becomes markedly lighter.

For high-power processors, flat-shaped heat pipes play a vital role inreducing the hotspot temperature. The most prominent solution is todeploy the disk-shaped heat pipe to reduce the hotspot temperature dueto the high-power consumption.

The square-shaped heat pipe (100×100 mm²) has the superior thermalperformance compared with other rectangular-shaped heat pipeconfigurations. However, the impact of the change in the configurationfrom square to rectangular is not that significant.

A copper heat spreader in the 3D IC structure can be replaced by therectangular-shaped or disk-shaped heat pipe to further optimize thethermal performance. Within the scope of the current study, thisreplacement reduces the hotspot temperature by 13 K or 17 K,respectively.

It can be appreciated that the embodiments disclosed herein can beimplemented in a number of systems and devices, and in the manufacturingof such systems and devices. Examples of systems/devices in which one ormore of the embodiments may be implemented include mobile devices andNAND flash memory chips. One example where the disclosed 3D IC (forexample, as a 3D IC chip) may find usefulness is in a handheld gameconsole such as the Sony PlayStation Portable (PSB). The Sony PSB caninclude hardware, for example, such as eDRAM (embedded DRAM) memory in a3D IC chip (e.g., a 3D system-in-package chip) with two dies stackedvertically. This semi-embedded DRAM arrangement has also been referredto as a ‘chip-on-chip’ (CoC) solution. Other examples where theembodiments can be implemented include multi-layer 3D IC's, embeddedNAND flash memory, and multi-chip package and package on packagesolutions for NAND flash memory in mobile devices. Other devices inwhich the embodiments can be implemented include High Bandwidth Memory(HBM) including stacked chips and TSVs.

It will be appreciated that variations of the above-disclosed and otherfeatures and functions, or alternatives thereof, may be desirablycombined into many other different systems or applications. It will alsobe appreciated that various presently unforeseen or unanticipatedalternatives, modifications, variations or improvements therein may besubsequently made by those skilled in the art which are also intended tobe encompassed by the following claims.

NOMENCLATURE c_(p) Specific heat at constant pressure [J (kg · K)⁻¹]f(x) Position of the maximum value of vapor velocity in y direction [m]h Height [m] h_(b) ⁺ Dimensionless half width of any of the vaporchannels, b/h h_(w) Thickness of the wick [m] k Thermal conductivity [W(m · K)⁻¹] K Permeability [m²] k_(eff) Effective thermal conductivity [W(m · K)⁻¹] l Length of the heat pipe [m] L_(eff) Effective length [m]L_(c) Characteristic length [m] n Normal coordinate p Pressure [Pa]Δp_(l) Overall liquid pressure drop along the heat pipe [Pa] Δp_(v)Overall vapor pressure drop along the heat pipe [Pa] Pe_(h) Pecletnumber q Heat flux [W · m⁻²] {dot over (q)}_(g) Volumetric heatgeneration rate [W · m⁻³] r coordinate R Radius of the disk-shaped heatpipe [m] Re_(h) Reynolds number T Temperature [K] u x-component ofvelocity [m · s⁻¹] v y-component of velocity [m · s⁻¹] w z-component ofvelocity [m · s⁻¹] x, y, z Cartesian coordinates Greek symbols φ Ratioof the evaporator length to the heat pipe length ν Kinematic viscosityof the vapor [m² · s⁻¹] Θ Dimensionless temperature ρ Density [kg · m⁻³]μ Dynamic viscosity [(N · s)m⁻²] Subscripts f Fluid m Mean e Evaporatorc Condenser l Liquid phase v Vapor phase w Wick 0 Initial Superscripts +Dimensionless quantities

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What is claimed is:
 1. A 3D integrated circuit device, comprising: asubstrate; a thermal interface material layer configured above thesubstrate; a plurality of die, a device layer and a micro-bump thermalinterface material layer formed above thermal interface material layer;a heat spreader located above the plurality of die, the device layer andthe thermal interface material, the heat spreader comprising a heat pipecomprising a rectangular-shaped heat pipe or disk-shaped heat pipe; anda heat sink located above the heat spreader, the heat sink comprisingthe heat pipe comprising the rectangular-shaped heat pipe or thedisk-shaped heat pipe.
 2. The 3D integrated circuit device wherein thethermal interface layer comprises a C4 bump.
 3. A 3D integrated circuitdevice, comprising: a substrate; a thermal interface material layercomprising C4 bumps; a plurality of die, a device layer and a micro-bumpthermal interface material layer formed above the C4-bump thermalinterface material layer; a heat spreader located above the plurality ofdie, the device layer and the thermal interface material, the heatspreader comprising a heat pipe comprising a rectangular-shaped heatpipe or disk-shaped heat pipe; and a heat sink located above the heatspreader, the heat sink comprising the heat pipe comprising therectangular-shaped heat pipe or the disk-shaped heat pipe.